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%I #7 Dec 10 2016 03:08:03
%S 0,1,7,1,1,1,1,1,5,1,1,9,4,13,4,1,2,27,1,28,1,2,2,3,2,7,1,1,19,1,8,3,
%T 3,2,1,10,1,1,1,1,1,1,2,3,1,1,35,1,2,91,1,1,1,4,1,1,1,1,1,2,16,1,2,2,
%U 1,2,6,1,1,6,14,1,5,5,14,2,8,1,1,1,1,2,4,2,10,37,1,10,2,4,5,4,5,24,1,2,7,1
%N Continued fraction for L(3, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3.
%C Contributed to OEIS on April 15, 2007 -- the 300th anniversary of the birth of Leonhard Euler.
%D Leonhard Euler, "Introductio in Analysin Infinitorum", First Part, Articles 176 and 292
%F chi3(k) = Kronecker(-3, k); chi3(k) is 0, 1, -1 when k reduced modulo 3 is 0, 1, 2, respectively; chi3 is A049347 shifted.
%F Series: L(3, chi3) = Sum_{k>=1} chi3(k) k^{-3} = 1 - 1/2^3 + 1/4^3 - 1/5^3 + 1/7^3 - 1/8^3 + 1/10^3 - 1/11^3 + ...
%F Closed form: L(3, chi3) = 4 Pi^3/(81 sqrt(3)).
%e L(3, chi3) = 0.8840238117500798567430579168710118077... = [0; 1, 7, 1, 1, 1, 1, 1, 5, 1, 1, 9, 4, 13, 4, ...].
%t nmax = 1000; ContinuedFraction[4 Pi^3/(81 Sqrt[3]), nmax + 1]
%Y Cf. A129404, A129405, A129406, A129407, A129409, A129410, A129411.
%Y Cf. A129658, A129659, A129660, A129661, A129662, A129663, A129664, A129665.
%K nonn,cofr,easy
%O 0,3
%A _Stuart Clary_, Apr 15 2007
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